The setting is similar to the seminar model of [1]}, each agent \(i\)  solves a dynamic programming problem at each period \(t\)  with a flow utility for the set of actions \(a_{it}=0\)  or 1:
\( U_{i0}(x_{it},a_{it-1}) = \varepsilon _{it}(0), \quad U_{i1}(x_{it},a_{it-1}) = \beta _{0i} + \beta _{1i}x_{it} -(1-a_{it-1})\delta _1 + \varepsilon _{it}(1), \) 
